As long as the wall wart has safety markings i.e. UL CSA etc, and is under 24V (SELV) your good to go. An input fuse would be a good idea anyway.
Ground is mainly provided for safety. If you have EMI RFI, ground loops, then a good filtered barrier strip might be an idea.

edit> hopefully the DC input has some EMI filter/s on the amp?
Switching amps are sources of noise so conn to grounds would make other things worse, unless you have very elaborate real earth grounds.

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like four million tons of hydrogen exploding on the sun
like the whisper of the termites building castles in the dust

We're talking very low voltages here, around 12 volts, so it really doesn't matter. The AMP 6 BASIC has an input fuse already on the board, and there's basically no way you can damage them if you soldered everything in right.

Sturdy little buggers. I used mine on festivals where you in the mornings could see dew dripping off the board it was so damp, and the sound was still perfect.